Pension Pay Out Choices

I am approaching the time when I will have to choose how to choose to take one defined benefit pension to which I am entitled. I can choose single life (me), at the highest payout, or a variation of spouse for life benefits upon my death (50%, 75%, 100%), for lesser amounts. This pension will produce roughly $3,000 per month or $36,000/yr at the 100% spousal level (i.e. my wife would continue to get the same amount of $$ per month as we both were until her death). Doing this would produce about $70K income per year while we are both alive, and about $50K per year for either of us, should one of us die.

I am concerned that my wife might be penalized income-wise were I the one to go into a nursing home and apply for Medicaid.

If I choose the 100% level spousal option, is the pension check treated as joint income, i.e. 50% each, so $1500 per month income would be attributed to each of us. Does my wife’s name have to be on each pension check or does the fact that she is legally entitled to the same payout upon my